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<a name="boost.random.niederreiter_base2_engine"></a><div class="titlepage"></div>
<div class="refnamediv">
<h2><span class="refentrytitle">Class template niederreiter_base2_engine</span></h2>
<p>boost::random::niederreiter_base2_engine</p>
</div>
<h2 class="refsynopsisdiv-title">Synopsis</h2>
<div class="refsynopsisdiv"><pre class="synopsis"><span class="comment">// In header: &lt;<a class="link" href="../../boost_random/reference.html#header.boost.random.niederreiter_base2_hpp" title="Header &lt;boost/random/niederreiter_base2.hpp&gt;">boost/random/niederreiter_base2.hpp</a>&gt;

</span><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> UIntType<span class="special">,</span> <span class="keyword">unsigned</span> w<span class="special">,</span> 
         <span class="keyword">typename</span> Nb2Table <span class="special">=</span> <span class="identifier">default_niederreiter_base2_table</span><span class="special">&gt;</span> 
<span class="keyword">class</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">{</span>
<span class="keyword">public</span><span class="special">:</span>
  <span class="comment">// types</span>
  <span class="keyword">typedef</span> <span class="identifier">UIntType</span> <a name="boost.random.niederreiter_base2_engine.result_type"></a><span class="identifier">result_type</span><span class="special">;</span>

  <span class="comment">// <a class="link" href="niederreiter_base2_engine.html#boost.random.niederreiter_base2_engineconstruct-copy-destruct">construct/copy/destruct</a></span>
  <span class="keyword">explicit</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_5-bb"><span class="identifier">niederreiter_base2_engine</span></a><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span><span class="special">)</span><span class="special">;</span>

  <span class="comment">// <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_4-bb">public member functions</a></span>
  <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_4_1-bb"><span class="identifier">dimension</span></a><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span>
  <span class="keyword">void</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_4_2-bb"><span class="identifier">seed</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span>
  <span class="keyword">void</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_4_3-bb"><span class="identifier">seed</span></a><span class="special">(</span><span class="identifier">UIntType</span><span class="special">)</span><span class="special">;</span>
  <span class="identifier">result_type</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_4_4-bb"><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span>
  <span class="keyword">void</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_4_5-bb"><span class="identifier">discard</span></a><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span><span class="special">)</span><span class="special">;</span>

  <span class="comment">// <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_6-bb">public static functions</a></span>
  <span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_6_1-bb"><span class="identifier">min</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span>
  <span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_6_2-bb"><span class="identifier">max</span></a><span class="special">(</span><span class="special">)</span><span class="special">;</span>

  <span class="comment">// <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_7-bb">friend functions</a></span>
  <span class="keyword">bool</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_7_1-bb"><span class="keyword">operator</span><span class="special">==</span></a><span class="special">(</span><span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span><span class="special">,</span> 
                  <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  <span class="keyword">bool</span> <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_7_2-bb"><span class="keyword">operator</span><span class="special">!=</span></a><span class="special">(</span><span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span><span class="special">,</span> 
                  <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">&gt;</span> 
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span> 
    <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_7_3-bb"><span class="keyword">operator</span><span class="special">&lt;&lt;</span></a><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span><span class="special">,</span> 
               <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
  <span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">&gt;</span> 
    <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span> 
    <a class="link" href="niederreiter_base2_engine.html#id-1_3_33_5_6_29_1_1_1_7_4-bb"><span class="keyword">operator</span><span class="special">&gt;&gt;</span></a><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span><span class="special">,</span> 
               <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span><span class="special">)</span><span class="special">;</span>
<span class="special">}</span><span class="special">;</span></pre></div>
<div class="refsect1">
<a name="id-1.3.33.5.6.28.3.4"></a><h2>Description</h2>
<p>Instantiations of class template <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> model a  <a class="link" href="../../boost_random/reference.html#boost_random.reference.concepts.quasi_random_number_generator" title="Quasi-Random Number Generator">quasi-random number generator</a> . The <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> uses the algorithm described in  </p>
<div class="blockquote"><blockquote class="blockquote"><p>  Bratley, Fox, Niederreiter, ACM Trans. Model. Comp. Sim. 2, 195 (1992).  </p></blockquote></div>
<p> </p>
<div class="note"><table border="0" summary="Note">
<tr>
<td rowspan="2" align="center" valign="top" width="25"><img alt="[Note]" src="../../../../doc/src/images/note.png"></td>
<th align="left">Note</th>
</tr>
<tr><td align="left" valign="top">
<p><a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> skips trivial zeroes at the start of the sequence. For example, the beginning of the 2-dimensional Niederreiter base 2 sequence in <code class="computeroutput"><a class="link" href="uniform_01.html" title="Class template uniform_01">uniform_01</a></code> distribution will look like this: </p>
<pre class="programlisting"><span class="number">0</span><span class="special">.</span><span class="number">5</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">5</span><span class="special">,</span>
<span class="number">0</span><span class="special">.</span><span class="number">75</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">25</span><span class="special">,</span>
<span class="number">0</span><span class="special">.</span><span class="number">25</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">75</span><span class="special">,</span>
<span class="number">0</span><span class="special">.</span><span class="number">375</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">375</span><span class="special">,</span>
<span class="number">0</span><span class="special">.</span><span class="number">875</span><span class="special">,</span> <span class="number">0</span><span class="special">.</span><span class="number">875</span><span class="special">,</span>
<span class="special">...</span>
</pre>
</td></tr>
</table></div>
<p>
In the following documentation <code class="computeroutput">X</code> denotes the concrete class of the template <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> returning objects of type <code class="computeroutput">UIntType</code>, u and v are the values of <code class="computeroutput">X</code>.</p>
<p>Some member functions may throw exceptions of type std::range_error. This happens when the quasi-random domain is exhausted and the generator cannot produce any more values. The length of the low discrepancy sequence is given by <span class="inlinemediaobject"><img src="../../images/random//form_31.png"></span>. </p>
<div class="refsect2">
<a name="id-1.3.33.5.6.28.3.4.5"></a><h3>
<a name="boost.random.niederreiter_base2_engineconstruct-copy-destruct"></a><code class="computeroutput">niederreiter_base2_engine</code> 
        public
       construct/copy/destruct</h3>
<div class="orderedlist"><ol class="orderedlist" type="1"><li class="listitem">
<pre class="literallayout"><span class="keyword">explicit</span> <a name="id-1_3_33_5_6_29_1_1_1_5-bb"></a><span class="identifier">niederreiter_base2_engine</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> s<span class="special">)</span><span class="special">;</span></pre>
<p>Effects: Constructs the default <code class="computeroutput">s</code>-dimensional Niederreiter base 2 quasi-random number generator.</p>
<p>Throws: bad_alloc, invalid_argument, range_error. </p>
</li></ol></div>
</div>
<div class="refsect2">
<a name="id-1.3.33.5.6.28.3.4.6"></a><h3>
<a name="id-1_3_33_5_6_29_1_1_1_4-bb"></a><code class="computeroutput">niederreiter_base2_engine</code> public member functions</h3>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
<pre class="literallayout"><span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <a name="id-1_3_33_5_6_29_1_1_1_4_1-bb"></a><span class="identifier">dimension</span><span class="special">(</span><span class="special">)</span> <span class="keyword">const</span><span class="special">;</span></pre>
<p>Returns: The dimension of of the quasi-random domain.</p>
<p>Throws: nothing. </p>
</li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">void</span> <a name="id-1_3_33_5_6_29_1_1_1_4_2-bb"></a><span class="identifier">seed</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre>Throws: nothing. <p>Effects: Resets the quasi-random number generator state to the one given by the default construction. Equivalent to u.seed(0). </p>
</li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">void</span> <a name="id-1_3_33_5_6_29_1_1_1_4_3-bb"></a><span class="identifier">seed</span><span class="special">(</span><span class="identifier">UIntType</span> init<span class="special">)</span><span class="special">;</span></pre>Throws: range_error. <p>Effects: Effectively sets the quasi-random number generator state to the <code class="computeroutput">init</code>-th vector in the <code class="computeroutput">s</code>-dimensional quasi-random domain, where <code class="computeroutput">s</code> == X::dimension(). </p>
<pre class="programlisting"><span class="identifier">X</span> <span class="identifier">u</span><span class="special">,</span> <span class="identifier">v</span><span class="special">;</span>
<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="identifier">N</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
    <span class="keyword">for</span><span class="special">(</span> <span class="identifier">std</span><span class="special">::</span><span class="identifier">size_t</span> <span class="identifier">j</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">j</span> <span class="special">&lt;</span> <span class="identifier">u</span><span class="special">.</span><span class="identifier">dimension</span><span class="special">(</span><span class="special">)</span><span class="special">;</span> <span class="special">++</span><span class="identifier">j</span> <span class="special">)</span>
        <span class="identifier">u</span><span class="special">(</span><span class="special">)</span><span class="special">;</span>
<span class="identifier">v</span><span class="special">.</span><span class="identifier">seed</span><span class="special">(</span><span class="identifier">N</span><span class="special">)</span><span class="special">;</span>
<span class="identifier">assert</span><span class="special">(</span><span class="identifier">u</span><span class="special">(</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">v</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span>
</pre>
<p> </p>
</li>
<li class="listitem">
<pre class="literallayout"><span class="identifier">result_type</span> <a name="id-1_3_33_5_6_29_1_1_1_4_4-bb"></a><span class="keyword">operator</span><span class="special">(</span><span class="special">)</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre>
<p>Returns: Returns a successive element of an <code class="computeroutput">s</code>-dimensional (s = X::dimension()) vector at each invocation. When all elements are exhausted, X::operator() begins anew with the starting element of a subsequent <code class="computeroutput">s</code>-dimensional vector.</p>
<p>Throws: range_error. </p>
</li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">void</span> <a name="id-1_3_33_5_6_29_1_1_1_4_5-bb"></a><span class="identifier">discard</span><span class="special">(</span><span class="identifier">boost</span><span class="special">::</span><span class="identifier">uintmax_t</span> z<span class="special">)</span><span class="special">;</span></pre>
<p>Effects: Advances *this state as if <code class="computeroutput">z</code> consecutive X::operator() invocations were executed. </p>
<pre class="programlisting"><span class="identifier">X</span> <span class="identifier">u</span> <span class="special">=</span> <span class="identifier">v</span><span class="special">;</span>
<span class="keyword">for</span><span class="special">(</span><span class="keyword">int</span> <span class="identifier">i</span> <span class="special">=</span> <span class="number">0</span><span class="special">;</span> <span class="identifier">i</span> <span class="special">&lt;</span> <span class="identifier">N</span><span class="special">;</span> <span class="special">++</span><span class="identifier">i</span><span class="special">)</span>
    <span class="identifier">u</span><span class="special">(</span><span class="special">)</span><span class="special">;</span>
<span class="identifier">v</span><span class="special">.</span><span class="identifier">discard</span><span class="special">(</span><span class="identifier">N</span><span class="special">)</span><span class="special">;</span>
<span class="identifier">assert</span><span class="special">(</span><span class="identifier">u</span><span class="special">(</span><span class="special">)</span> <span class="special">==</span> <span class="identifier">v</span><span class="special">(</span><span class="special">)</span><span class="special">)</span><span class="special">;</span>
</pre>
<p>Throws: range_error. </p>
</li>
</ol></div>
</div>
<div class="refsect2">
<a name="id-1.3.33.5.6.28.3.4.7"></a><h3>
<a name="id-1_3_33_5_6_29_1_1_1_6-bb"></a><code class="computeroutput">niederreiter_base2_engine</code> public static functions</h3>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
<pre class="literallayout"><span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a name="id-1_3_33_5_6_29_1_1_1_6_1-bb"></a><span class="identifier">min</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre>
<p>Returns: Tight lower bound on the set of values returned by operator().</p>
<p>Throws: nothing. </p>
</li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">static</span> <span class="keyword">constexpr</span> <span class="identifier">result_type</span> <a name="id-1_3_33_5_6_29_1_1_1_6_2-bb"></a><span class="identifier">max</span><span class="special">(</span><span class="special">)</span><span class="special">;</span></pre>
<p>Returns: Tight upper bound on the set of values returned by operator().</p>
<p>Throws: nothing. </p>
</li>
</ol></div>
</div>
<div class="refsect2">
<a name="id-1.3.33.5.6.28.3.4.8"></a><h3>
<a name="id-1_3_33_5_6_29_1_1_1_7-bb"></a><code class="computeroutput">niederreiter_base2_engine</code> friend functions</h3>
<div class="orderedlist"><ol class="orderedlist" type="1">
<li class="listitem">
<pre class="literallayout"><span class="keyword">bool</span> <a name="id-1_3_33_5_6_29_1_1_1_7_1-bb"></a><span class="keyword">operator</span><span class="special">==</span><span class="special">(</span><span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span> x<span class="special">,</span> 
                <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span> y<span class="special">)</span><span class="special">;</span></pre>Returns true if the two generators will produce identical sequences of outputs. </li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">bool</span> <a name="id-1_3_33_5_6_29_1_1_1_7_2-bb"></a><span class="keyword">operator</span><span class="special">!=</span><span class="special">(</span><span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span> lhs<span class="special">,</span> 
                <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span> rhs<span class="special">)</span><span class="special">;</span></pre>Returns true if the two generators will produce different sequences of outputs. </li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">&gt;</span> 
  <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span> 
  <a name="id-1_3_33_5_6_29_1_1_1_7_3-bb"></a><span class="keyword">operator</span><span class="special">&lt;&lt;</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_ostream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span> os<span class="special">,</span> 
             <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span> s<span class="special">)</span><span class="special">;</span></pre>Writes the textual representation of the generator to a <code class="computeroutput">std::ostream</code>. </li>
<li class="listitem">
<pre class="literallayout"><span class="keyword">template</span><span class="special">&lt;</span><span class="keyword">typename</span> CharT<span class="special">,</span> <span class="keyword">typename</span> Traits<span class="special">&gt;</span> 
  <span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span> 
  <a name="id-1_3_33_5_6_29_1_1_1_7_4-bb"></a><span class="keyword">operator</span><span class="special">&gt;&gt;</span><span class="special">(</span><span class="identifier">std</span><span class="special">::</span><span class="identifier">basic_istream</span><span class="special">&lt;</span> <span class="identifier">CharT</span><span class="special">,</span> <span class="identifier">Traits</span> <span class="special">&gt;</span> <span class="special">&amp;</span> is<span class="special">,</span> 
             <span class="keyword">const</span> <a class="link" href="niederreiter_base2_engine.html" title="Class template niederreiter_base2_engine">niederreiter_base2_engine</a> <span class="special">&amp;</span> s<span class="special">)</span><span class="special">;</span></pre>Reads the textual representation of the generator from a <code class="computeroutput">std::istream</code>. </li>
</ol></div>
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<div class="copyright-footer">Copyright © 2000-2005 Jens Maurer<br>Copyright © 2009, 2010 Steven Watanabe<p>
        Distributed under the Boost Software License, Version 1.0. (See accompanying
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